The reflectivity spectrum of a Fiber Bragg Grating with uniform modulation of refractive index is followed by a series of sidelobes at adjacent wavelengths. An efficient method to minimize these unwanted sidelobes is to increase gradually the coupling coefficient into the grating entrance, and decrease it gradually until the grating end. It is possible to vary the amplitude of the coupling coefficient along the length using an apodization function. This paper presents the development of an analytical formulation of the grating reflectivity to analyze the sidelobe reduction dependence on the apodization function. Additionally, simulations were performed to studying the grating peak reflectivity dependence on the apodization function and grating length.